What is (\partial)/(\partial x)(1/t e^{(x^2)/(4t)}) ?

The answer to (\partial)/(\partial x)(1/t e^{(x^2)/(4t)}) is (e^{\frac{x^2)/(4t)}x}{2t^2}

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(\partial)/(\partial x)(1/t e^{(x^2)/(4t)})

\frac{\partial}{\partial x} (\frac{1}{t} e^{\frac{x ^{2}}{4 t}})

\frac{e ^{\frac{x ^{2}}{4 t}} x}{2 t ^{2}}

Solution steps

\frac{\partial}{\partial x} (\frac{1}{t} e^{\frac{x ^{2}}{4 t}})

Treat

t

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= \frac{1}{t} \frac{\partial}{\partial x} (e^{\frac{x ^{2}}{4 t}})

Apply the chain rule:

e^{\frac{x ^{2}}{4 t}} \frac{\partial}{\partial x} (\frac{x ^{2}}{4 t})

= e^{\frac{x ^{2}}{4 t}} \frac{\partial}{\partial x} (\frac{x ^{2}}{4 t})

\frac{\partial}{\partial x} (\frac{x ^{2}}{4 t}) = \frac{x}{2 t}

= \frac{1}{t} e^{\frac{x ^{2}}{4 t}} \frac{x}{2 t}

Simplify

\frac{1}{t} e^{\frac{x ^{2}}{4 t}} \frac{x}{2 t} : \frac{e ^{\frac{x ^{2}}{4 t}} x}{2 t ^{2}}

= \frac{e ^{\frac{x ^{2}}{4 t}} x}{2 t ^{2}}

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What is (\partial)/(\partial x)(1/t e^{(x^2)/(4t)}) ?
The answer to (\partial)/(\partial x)(1/t e^{(x^2)/(4t)}) is (e^{\frac{x^2)/(4t)}x}{2t^2}